JUMPING Your Strength determines how far you can jump.
Long Jump. When you make a long jump, you cover a number of feet up to your Strength score if you move at least 10 feet on foot immediately before the jump. When you make a standing long jump, you can leap only half that distance. Either way, each foot you clear on the jump costs a foot of movement.
This rule assumes that the height of your jump doesn’t matter, such as a jump across a stream or chasm. At your DM’s option, you must succeed on a DC 10 Strength (Athletics) check to clear a low obstacle (no taller than a quarter of the jump’s distance), such as a hedge or low wall. Otherwise, you hit it.
When you land in difficult terrain, you must succeed on a DC 10 Dexterity (Acrobatics) check to land on your feet. Otherwise, you land prone.
High Jump. When you make a high jump, you leap into the air a number of feet equal to 3 + your Strength modifier if you move at least 10 feet on foot immediately before the jump. When you make a standing high jump, you can jump only half that distance. Either way, each foot you clear on the jump costs a foot of movement. In some circumstances, your DM might allow you to make a Strength (Athletics) check to jump higher than you normally can.
You can extend your arms half your height above yourself during the jump. Thus, you can reach above you a distance equal to the height of the jump plus 1. times your height.
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Athletics. Your Strength (Athletics) check covers difficult situations you encounter while climbing, jumping, or swimming. Examples include the following activities:
-You try to jump an unusually long distance or pull off a stunt midjump.
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The above are the specific rules for jumping, anything else is up to the DM.
The way I handle a strength 15 character making a long jump of of 16' or 20', is by making them make a Strength(athletics) check as it states. DC varies by situation but a 15 will get you a few extra feet at my table. I also allow the extension of arms like with a high jump on a long jump so the 16' gap would be withing reach just clinging to the side.
I take extra movement, height, size and stuff into adjudicating the above DC for extra distance covered.
Landing in difficult terrain as above is a DC 10 Dexterity(acrobatics) check to land not prone.
But if the character has the strength and the 10 feet of room for a jump a strength 15 halfling makes a 15' jump without a check, because that is what the rules say happens. Pretty much 10' wide pits in the hall don't matter much unless someone dumped strength to less than 10.